IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i8p1129-d1372681.html
   My bibliography  Save this article

On Complex Pisot Numbers That Are Roots of Borwein Trinomials

Author

Listed:
  • Paulius Drungilas

    (Institute of Mathematics, Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Jonas Jankauskas

    (Institute of Mathematics, Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Grintas Junevičius

    (Institute of Mathematics, Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

Let n > m be positive integers. Polynomials of the form z n ± z m ± 1 are called Borwein trinomials. Using an old result of Bohl, we derive explicit formulas for the number of roots of a Borwein trinomial inside the unit circle | z | < 1 . Based on this, we determine all Borwein trinomials that have a complex Pisot number as a root. There are exactly 29 such trinomials.

Suggested Citation

  • Paulius Drungilas & Jonas Jankauskas & Grintas Junevičius, 2024. "On Complex Pisot Numbers That Are Roots of Borwein Trinomials," Mathematics, MDPI, vol. 12(8), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1129-:d:1372681
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/8/1129/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/8/1129/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1129-:d:1372681. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.